diff --git a/Autoupdate/SPUDeltaArchive.m b/Autoupdate/SPUDeltaArchive.m
index ca7ade75a..e2f1e40b8 100644
--- a/Autoupdate/SPUDeltaArchive.m
+++ b/Autoupdate/SPUDeltaArchive.m
@@ -89,8 +89,9 @@ @implementation SPUDeltaArchiveHeader
 @synthesize fileSystemCompression = _fileSystemCompression;
 @synthesize majorVersion = _majorVersion;
 @synthesize minorVersion = _minorVersion;
+@synthesize bundleCreationDate = _bundleCreationDate;
 
-- (instancetype)initWithCompression:(SPUDeltaCompressionMode)compression compressionLevel:(uint8_t)compressionLevel fileSystemCompression:(bool)fileSystemCompression majorVersion:(uint16_t)majorVersion minorVersion:(uint16_t)minorVersion beforeTreeHash:(const unsigned char *)beforeTreeHash afterTreeHash:(const unsigned char *)afterTreeHash
+- (instancetype)initWithCompression:(SPUDeltaCompressionMode)compression compressionLevel:(uint8_t)compressionLevel fileSystemCompression:(bool)fileSystemCompression majorVersion:(uint16_t)majorVersion minorVersion:(uint16_t)minorVersion beforeTreeHash:(const unsigned char *)beforeTreeHash afterTreeHash:(const unsigned char *)afterTreeHash bundleCreationDate:(nullable NSDate *)bundleCreationDate
 {
     self = [super init];
     if (self != nil)
@@ -104,6 +105,8 @@ - (instancetype)initWithCompression:(SPUDeltaCompressionMode)compression compres
         
         memcpy(_beforeTreeHash, beforeTreeHash, sizeof(_beforeTreeHash));
         memcpy(_afterTreeHash, afterTreeHash, sizeof(_afterTreeHash));
+        
+        _bundleCreationDate = bundleCreationDate;
     }
     return self;
 }
diff --git a/Autoupdate/SPUDeltaArchiveProtocol.h b/Autoupdate/SPUDeltaArchiveProtocol.h
index 606908c0e..f601266b1 100644
--- a/Autoupdate/SPUDeltaArchiveProtocol.h
+++ b/Autoupdate/SPUDeltaArchiveProtocol.h
@@ -26,7 +26,7 @@ typedef NS_ENUM(uint8_t, SPUDeltaItemCommands) {
 // Represents header for our archive
 SPU_OBJC_DIRECT_MEMBERS @interface SPUDeltaArchiveHeader : NSObject
 
-- (instancetype)initWithCompression:(SPUDeltaCompressionMode)compression compressionLevel:(uint8_t)compressionLevel fileSystemCompression:(bool)fileSystemCompression majorVersion:(uint16_t)majorVersion minorVersion:(uint16_t)minorVersion beforeTreeHash:(const unsigned char *)beforeTreeHash afterTreeHash:(const unsigned char *)afterTreeHash;
+- (instancetype)initWithCompression:(SPUDeltaCompressionMode)compression compressionLevel:(uint8_t)compressionLevel fileSystemCompression:(bool)fileSystemCompression majorVersion:(uint16_t)majorVersion minorVersion:(uint16_t)minorVersion beforeTreeHash:(const unsigned char *)beforeTreeHash afterTreeHash:(const unsigned char *)afterTreeHash bundleCreationDate:(nullable NSDate *)bundleCreationDate;
 
 @property (nonatomic, readonly) SPUDeltaCompressionMode compression;
 @property (nonatomic, readonly) uint8_t compressionLevel;
@@ -35,6 +35,7 @@ SPU_OBJC_DIRECT_MEMBERS @interface SPUDeltaArchiveHeader : NSObject
 @property (nonatomic, readonly) uint16_t minorVersion;
 @property (nonatomic, readonly) unsigned char *beforeTreeHash;
 @property (nonatomic, readonly) unsigned char *afterTreeHash;
+@property (nonatomic, readonly, nullable) NSDate *bundleCreationDate;
 
 @end
 
diff --git a/Autoupdate/SPUSparkleDeltaArchive.m b/Autoupdate/SPUSparkleDeltaArchive.m
index cb71c73c2..f85019843 100644
--- a/Autoupdate/SPUSparkleDeltaArchive.m
+++ b/Autoupdate/SPUSparkleDeltaArchive.m
@@ -348,7 +348,19 @@ - (nullable SPUDeltaArchiveHeader *)readHeader
         return nil;
     }
     
-    return [[SPUDeltaArchiveHeader alloc] initWithCompression:compression compressionLevel:metadata.compressionLevel fileSystemCompression:metadata.fileSystemCompression majorVersion:majorVersion minorVersion:minorVersion beforeTreeHash:beforeTreeHash afterTreeHash:afterTreeHash];
+    NSDate *bundleCreationDate;
+    if (MAJOR_VERSION_IS_AT_LEAST(majorVersion, SUBinaryDeltaMajorVersion4)) {
+        double bundleCreationTimeInterval = 0;
+        if (![self _readBuffer:&bundleCreationTimeInterval length:sizeof(bundleCreationTimeInterval)]) {
+            return nil;
+        }
+        
+        bundleCreationDate = (bundleCreationTimeInterval != 0.0) ? [NSDate dateWithTimeIntervalSinceReferenceDate:bundleCreationTimeInterval] : nil;
+    } else {
+        bundleCreationDate = nil;
+    }
+    
+    return [[SPUDeltaArchiveHeader alloc] initWithCompression:compression compressionLevel:metadata.compressionLevel fileSystemCompression:metadata.fileSystemCompression majorVersion:majorVersion minorVersion:minorVersion beforeTreeHash:beforeTreeHash afterTreeHash:afterTreeHash bundleCreationDate:bundleCreationDate];
 }
 
 - (NSArray<NSString *> *)_readRelativeFilePaths SPU_OBJC_DIRECT
@@ -855,6 +867,14 @@ - (void)writeHeader:(SPUDeltaArchiveHeader *)header
     
     [self _writeBuffer:header.beforeTreeHash length:CC_SHA1_DIGEST_LENGTH];
     [self _writeBuffer:header.afterTreeHash length:CC_SHA1_DIGEST_LENGTH];
+    
+    if (MAJOR_VERSION_IS_AT_LEAST(majorVersion, SUBinaryDeltaMajorVersion4)) {
+        NSDate *bundleCreationDate = header.bundleCreationDate;
+        
+        // If bundleCreationDate == nil, we will write out a 0 time interval
+        double timeInterval = bundleCreationDate.timeIntervalSinceReferenceDate;
+        [self _writeBuffer:&timeInterval length:sizeof(timeInterval)];
+    }
 }
 
 - (void)addItem:(SPUDeltaArchiveItem *)item
@@ -883,7 +903,7 @@ - (void)finishEncodingItems
     
     // Clone commands reference relative file paths in this table but sometimes there may not
     // be an entry if extraction for an original item was skipped. Fill out any missing file path entries.
-    // For example, if A.app has Contents/A and B.app has Contents/A and Contents/A and Contents/B,
+    // For example, if A.app has Contents/A and B.app has Contents/A and Contents/B,
     // where A and B's contents are the same and A is the same in both apps, normally we would not record Contents/A because its extraction was skipped. However now B is a clone of A so we need a record for A.
     NSMutableArray<NSString *> *newClonedPathEntries = [NSMutableArray array];
     for (SPUDeltaArchiveItem *item in writableItems) {
diff --git a/Autoupdate/SPUXarDeltaArchive.m b/Autoupdate/SPUXarDeltaArchive.m
index ab117230d..cb859c7ae 100644
--- a/Autoupdate/SPUXarDeltaArchive.m
+++ b/Autoupdate/SPUXarDeltaArchive.m
@@ -167,7 +167,7 @@ - (nullable SPUDeltaArchiveHeader *)readHeader
     
     // I wasn't able to figure out how to retrieve the compression options from xar,
     // so we will use default flags to indicate the info isn't available
-    return [[SPUDeltaArchiveHeader alloc] initWithCompression:SPUDeltaCompressionModeDefault compressionLevel:0 fileSystemCompression:false majorVersion:majorDiffVersion minorVersion:minorDiffVersion beforeTreeHash:rawExpectedBeforeHash afterTreeHash:rawExpectedAfterHash];
+    return [[SPUDeltaArchiveHeader alloc] initWithCompression:SPUDeltaCompressionModeDefault compressionLevel:0 fileSystemCompression:false majorVersion:majorDiffVersion minorVersion:minorDiffVersion beforeTreeHash:rawExpectedBeforeHash afterTreeHash:rawExpectedAfterHash bundleCreationDate:nil];
 }
 
 - (void)writeHeader:(SPUDeltaArchiveHeader *)header
diff --git a/Autoupdate/SUBinaryDeltaApply.m b/Autoupdate/SUBinaryDeltaApply.m
index 9e862f1ff..f3a456131 100644
--- a/Autoupdate/SUBinaryDeltaApply.m
+++ b/Autoupdate/SUBinaryDeltaApply.m
@@ -152,6 +152,16 @@ BOOL applyBinaryDelta(NSString *source, NSString *finalDestination, NSString *pa
         }
         return NO;
     }
+    
+    // Preserve file creation date only for the root item if the date is recorded
+    // (requires major version 4 or later)
+    NSDate *bundleCreationDate = header.bundleCreationDate;
+    if (bundleCreationDate != nil) {
+        NSError *setFileCreationDateError = nil;
+        if (![fileManager setAttributes:@{NSFileCreationDate: bundleCreationDate} ofItemAtPath:destination error:&setFileCreationDateError]) {
+            fprintf(stderr, "\nWarning: failed to set file creation date: %s", setFileCreationDateError.localizedDescription.UTF8String);
+        }
+    }
 
     progressCallback(4/7.0);
 
diff --git a/Autoupdate/SUBinaryDeltaCommon.h b/Autoupdate/SUBinaryDeltaCommon.h
index e70aa1ce4..e6187ccc8 100644
--- a/Autoupdate/SUBinaryDeltaCommon.h
+++ b/Autoupdate/SUBinaryDeltaCommon.h
@@ -44,7 +44,8 @@ typedef NS_ENUM(uint16_t, SUBinaryDeltaMajorVersion)
     // Note: support for creating or applying version 1 deltas have been removed
     SUBinaryDeltaMajorVersion1 = 1,
     SUBinaryDeltaMajorVersion2 = 2,
-    SUBinaryDeltaMajorVersion3 = 3
+    SUBinaryDeltaMajorVersion3 = 3,
+    SUBinaryDeltaMajorVersion4 = 4,
 };
 
 extern SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionDefault;
@@ -52,8 +53,8 @@ extern SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionLatest;
 extern SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionFirst;
 extern SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionFirstSupported;
 
-// Additional compression methods for version 3 patches that we have for debugging are zlib, bzip2, none
-#define COMPRESSION_METHOD_ARGUMENT_DESCRIPTION @"The compression method to use for generating delta updates. Supported methods for version 3 delta files are 'lzma' (best compression, slowest), 'lzfse' (good compression, fast), 'lz4' (worse compression, fastest), and 'default'. Note that version 2 delta files only support 'bzip2', and 'default' so other methods will be ignored if version 2 files are being generated. The 'default' compression for version 3 delta files is currently lzma."
+// Additional compression methods for version 3 or 4 patches that we have for debugging are zlib, bzip2, none
+#define COMPRESSION_METHOD_ARGUMENT_DESCRIPTION @"The compression method to use for generating delta updates. Supported methods for version 3 delta files are 'lzma' (best compression, slowest), 'lzfse' (good compression, fast), 'lz4' (worse compression, fastest), and 'default'. Note that version 2 delta files only support 'bzip2', and 'default' so other methods will be ignored if version 2 files are being generated. The 'default' compression for version 3 or 4 delta files is currently lzma."
 
 //#define COMPRESSION_LEVEL_ARGUMENT_DESCRIPTION @"The compression level to use for generating delta updates. This only applies if the compression method used is bzip2 which accepts values from 1 - 9. A special value of 0 will use the default compression level."
 
diff --git a/Autoupdate/SUBinaryDeltaCommon.m b/Autoupdate/SUBinaryDeltaCommon.m
index d1c718c3f..0461b2d0f 100644
--- a/Autoupdate/SUBinaryDeltaCommon.m
+++ b/Autoupdate/SUBinaryDeltaCommon.m
@@ -22,7 +22,7 @@
 // Note: the framework bundle version must be bumped, and generate_appcast must be updated to compare it,
 // when we add/change new major versions and defaults. Unit tests need to be updated to use new versions too.
 SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionDefault = SUBinaryDeltaMajorVersion3;
-SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionLatest = SUBinaryDeltaMajorVersion3;
+SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionLatest = SUBinaryDeltaMajorVersion4;
 SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionFirst = SUBinaryDeltaMajorVersion1;
 SUBinaryDeltaMajorVersion SUBinaryDeltaMajorVersionFirstSupported = SUBinaryDeltaMajorVersion2;
 
@@ -115,6 +115,8 @@ uint16_t latestMinorVersionForMajorVersion(SUBinaryDeltaMajorVersion majorVersio
             return 4;
         case SUBinaryDeltaMajorVersion3:
             return 1;
+        case SUBinaryDeltaMajorVersion4:
+            return 0;
     }
     return 0;
 }
diff --git a/Autoupdate/SUBinaryDeltaCreate.m b/Autoupdate/SUBinaryDeltaCreate.m
index 925688c69..a94896334 100644
--- a/Autoupdate/SUBinaryDeltaCreate.m
+++ b/Autoupdate/SUBinaryDeltaCreate.m
@@ -723,7 +723,23 @@ BOOL createBinaryDelta(NSString *source, NSString *destination, NSString *patchF
 #endif
     }
     
-    SPUDeltaArchiveHeader *header = [[SPUDeltaArchiveHeader alloc] initWithCompression:compression compressionLevel:compressionLevel fileSystemCompression:foundFilesystemCompression majorVersion:majorVersion minorVersion:minorVersion beforeTreeHash:beforeHash afterTreeHash:afterHash];
+    // Record creation date of root bundle item
+    NSDate *bundleCreationDate;
+    if (MAJOR_VERSION_IS_AT_LEAST(majorVersion, SUBinaryDeltaMajorVersion4)) {
+        NSError *fileAttributesError = nil;
+        NSDictionary<NSFileAttributeKey, id> *fileAttributes = [[NSFileManager defaultManager] attributesOfItemAtPath:destination error:&fileAttributesError];
+        
+        if (fileAttributes != nil) {
+            bundleCreationDate = fileAttributes[NSFileCreationDate];
+        } else {
+            bundleCreationDate = nil;
+            fprintf(stderr, "\nWarning: unable to retrieve file creation date of new bundle: %s", fileAttributesError.localizedDescription.UTF8String);
+        }
+    } else {
+        bundleCreationDate = nil;
+    }
+    
+    SPUDeltaArchiveHeader *header = [[SPUDeltaArchiveHeader alloc] initWithCompression:compression compressionLevel:compressionLevel fileSystemCompression:foundFilesystemCompression majorVersion:majorVersion minorVersion:minorVersion beforeTreeHash:beforeHash afterTreeHash:afterHash bundleCreationDate:bundleCreationDate];
     
     [archive writeHeader:header];
     if (archive.error != nil) {
diff --git a/Tests/SUBinaryDeltaTest.m b/Tests/SUBinaryDeltaTest.m
index ecf19705f..97cdc842a 100644
--- a/Tests/SUBinaryDeltaTest.m
+++ b/Tests/SUBinaryDeltaTest.m
@@ -101,29 +101,32 @@ - (BOOL)createAndApplyPatchWithBeforeDiffHandler:(SUDeltaHandler)beforeDiffHandl
 #else
     BOOL testingVersion2Delta = NO;
 #endif
-    return [self createAndApplyPatchWithBeforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler testingVersion2Delta:testingVersion2Delta];
+    return [self createAndApplyPatchWithBeforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler testingVersion3Delta:YES testingVersion2Delta:testingVersion2Delta];
 }
 
-- (BOOL)createAndApplyPatchWithBeforeDiffHandler:(SUDeltaHandler)beforeDiffHandler afterDiffHandler:(SUDeltaHandler)afterDiffHandler afterPatchHandler:(SUDeltaHandler)afterPatchHandler testingVersion2Delta:(BOOL)testingVersion2Delta
+- (BOOL)createAndApplyPatchWithBeforeDiffHandler:(SUDeltaHandler)beforeDiffHandler afterDiffHandler:(SUDeltaHandler)afterDiffHandler afterPatchHandler:(SUDeltaHandler)afterPatchHandler testingVersion3Delta:(BOOL)testingVersion3Delta testingVersion2Delta:(BOOL)testingVersion2Delta
 {
-    XCTAssertEqual(SUBinaryDeltaMajorVersion3, SUBinaryDeltaMajorVersionLatest);
+    XCTAssertEqual(SUBinaryDeltaMajorVersion4, SUBinaryDeltaMajorVersionLatest);
     
-    BOOL version3DeltaFormatWithLZMASuccess = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion3 compressionMode:SPUDeltaCompressionModeLZMA beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
+    BOOL version4DeltaFormatWithLZMASuccess = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion4 compressionMode:SPUDeltaCompressionModeLZMA beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
     
 #if SPARKLE_BUILD_BZIP2_DELTA_SUPPORT
-    BOOL version3DeltaFormatWithBZIP2Success = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion3 compressionMode:SPUDeltaCompressionModeBzip2 beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
+    BOOL version4DeltaFormatWithBZIP2Success = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion4 compressionMode:SPUDeltaCompressionModeBzip2 beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
 #endif
     
-    BOOL version3DeltaFormatWithZLIBSuccess = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion3 compressionMode:SPUDeltaCompressionModeZLIB beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
+    BOOL version4DeltaFormatWithZLIBSuccess = [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion4 compressionMode:SPUDeltaCompressionModeZLIB beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
+    
+    BOOL version3DeltaFormatWithLZMASuccess = !testingVersion3Delta || [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion3 compressionMode:SPUDeltaCompressionModeLZMA beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
     
     BOOL version2FormatSuccess = !testingVersion2Delta || [self createAndApplyPatchUsingVersion:SUBinaryDeltaMajorVersion2 compressionMode:SPUDeltaCompressionModeDefault beforeDiffHandler:beforeDiffHandler afterDiffHandler:afterDiffHandler afterPatchHandler:afterPatchHandler];
     
     return (
-        version3DeltaFormatWithLZMASuccess &&
+        version4DeltaFormatWithLZMASuccess &&
 #if SPARKLE_BUILD_BZIP2_DELTA_SUPPORT
-        version3DeltaFormatWithBZIP2Success &&
+        version4DeltaFormatWithBZIP2Success &&
 #endif
-        version3DeltaFormatWithZLIBSuccess &&
+        version4DeltaFormatWithZLIBSuccess &&
+        version3DeltaFormatWithLZMASuccess &&
         version2FormatSuccess
     );
 }
@@ -1001,7 +1004,7 @@ - (void)testAddingSymlinkWithWrongPermissions
         // Test that we only respect valid symlink permissions for >= version 3 deltas
         unsigned short permissions = permissionAttribute.unsignedShortValue & PERMISSION_FLAGS;
         XCTAssertEqual(permissions, VALID_SYMBOLIC_LINK_PERMISSIONS);
-    } testingVersion2Delta:NO];
+    } testingVersion3Delta:YES testingVersion2Delta:NO];
 }
 
 - (void)testSmallFilePermissionChangeWithNoContentChange
@@ -1410,7 +1413,7 @@ - (void)testFileSystemCompression
                 XCTFail(@"Second destination file is not compressed!");
             }
         }
-    } testingVersion2Delta:NO];
+    } testingVersion3Delta:YES testingVersion2Delta:NO];
 }
 
 - (void)testNoFileSystemCompression
@@ -1455,7 +1458,7 @@ - (void)testNoFileSystemCompression
                 XCTFail(@"Second destination file is compressed!");
             }
         }
-    } testingVersion2Delta:NO];
+    } testingVersion3Delta:YES testingVersion2Delta:NO];
 }
 
 - (void)testFrameworkVersionChanged
@@ -2207,4 +2210,45 @@ - (void)testInvalidSparkleFrameworkInAfterTree
     XCTAssertFalse(success);
 }
 
+- (void)testBundleCreationDate
+{
+    NSDate *sourceDate = [NSDate dateWithTimeIntervalSinceReferenceDate:420111117.0];
+    NSDate *destinationDate = [NSDate dateWithTimeIntervalSinceReferenceDate:530112117.0];
+    
+    BOOL success = [self createAndApplyPatchWithBeforeDiffHandler:^(NSFileManager *fileManager, NSString *sourceDirectory, NSString *destinationDirectory) {
+        NSString *sourceFile = [sourceDirectory stringByAppendingPathComponent:@"A"];
+        NSString *destinationFile = [destinationDirectory stringByAppendingPathComponent:@"A"];
+        
+        XCTAssertTrue([[NSData data] writeToFile:sourceFile atomically:YES]);
+        XCTAssertTrue([[NSData dataWithBytes:"loltest" length:7] writeToFile:destinationFile atomically:YES]);
+        
+        {
+            NSError *setFileCreationDateError = nil;
+            if (![fileManager setAttributes:@{NSFileCreationDate: sourceDate} ofItemAtPath:sourceDirectory error:&setFileCreationDateError]) {
+                XCTFail(@"Failed to modify file creation date for source directory: %@", setFileCreationDateError.localizedDescription);
+            }
+        }
+        
+        {
+            NSError *setFileCreationDateError = nil;
+            if (![fileManager setAttributes:@{NSFileCreationDate: destinationDate} ofItemAtPath:destinationDirectory error:&setFileCreationDateError]) {
+                XCTFail(@"Failed to modify file creation date for destination directory: %@", setFileCreationDateError.localizedDescription);
+            }
+        }
+    } afterDiffHandler:nil afterPatchHandler:^(NSFileManager *fileManager, NSString * __unused sourceDirectory, NSString *destinationDirectory) {
+        NSError *fileAttributesError = nil;
+        NSDictionary<NSFileAttributeKey, id> *fileAttributes = [fileManager attributesOfItemAtPath:destinationDirectory error:&fileAttributesError];
+        
+        if (fileAttributes == nil) {
+            XCTFail(@"Failed to retrieve file attributes from destination directory: %@", fileAttributesError.localizedDescription);
+        }
+        
+        NSDate *fileCreationDate = fileAttributes[NSFileCreationDate];
+        XCTAssertNotNil(fileCreationDate);
+        
+        XCTAssertEqualObjects(destinationDate, fileCreationDate);
+    } testingVersion3Delta:NO testingVersion2Delta:NO];
+    XCTAssertTrue(success);
+}
+
 @end